Name
Title | ||
|---|---|---|
Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services |
Abstract | ||
|---|---|---|
AbstractAbstract In this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics the idle probability and the mean number of customers in the system of the systems considered with a given approximation error. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.2478/amcs-2018-0011 | Periodicals |
Keywords | Field | DocType |
inhomogeneous birth and death processes, weak ergodicity, rate of convergence, sharp bounds, logarithmic norm, forward Kolmogorov system | Mathematical optimization,Markov process,Queueing theory,Rate of convergence,Logarithmic norm,Mathematics | Journal |
Volume | Issue | ISSN |
28 | 1 | 1641-876X |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander I. Zeifman | 1 | 44 | 17.93 |
| Rostislav Razumchik | 2 | 9 | 9.46 |
| Yacov Satin | 3 | 9 | 5.24 |
| Ksenia Kiseleva | 4 | 0 | 0.68 |
| Anna Korotysheva | 5 | 11 | 5.32 |
| Victor Korolev | 6 | 16 | 11.26 |